Known in the state of the art are solutions for the construction from a set of data of rule-based explicative models. These methods are designed to determine the set of the best rules, i.e., the set of rules that collectively maximize certain quality criteria. A number of these solutions are based on stochastic optimization techniques (in which one searches for rules maximizing the quality by an alternation of random and deterministic displacements in the space of the possible rules) such as, e.g., genetic algorithms. The following publications can be cited as representative of this approach.
For a general introduction to the application of stochastic optimization to the construction of sets of rules:
A. A. Frietas (2003). A Survey of Evolutionary Algorithms for Data Mining and Knowledge Discovery. Advances in evolutionary computing: theory and applications, A. Ghosh and S. Tsutsui (eds.), pp. 819-845, Springer.
The representation of a rule by an individual of the population of a genetic algorithm was proposed by:
J. H. Holland (1986). Escape brittleness: the possibilities of general-purpose learning algorithms applied to rule-based systems. Machine Learning: an AI Approach, volume 3, R. S. Michalski, T. M. Mitchell, J. G. Carbonell and Y. Kodratoff (eds.), pp. 593-623, Morgan Kaufmann.
Other publications expanded this approach:
K. De Jong (1988). Learning with Genetic Algorithms: An overview. Machine Learning 3, pp. 121-138.
K. De Jong and W. M. Spears (1991). Learning, concept classification rules using genetic algorithms, Proceedings of the 12th International Joint Conference on Artificial intelligence, K. Mylopoulos and R. Reiter (eds.), pp. 651-656, Morgan Kaufman.
The problem posed by these solutions is twofold: on the one hand, these solutions are intended to calculate a model constituted of a set of rules and are not suitable for the development of a single rule and on the other hand the user cannot confront the result of the algorithmic processing with the user's own expertise. More precisely, the user cannot interact with the rule development process which results from an automatic processing not taking into account the user's empirical postulates.